SOLUTION: Find all the solutions of the equation z˄6 + (2 + 2i)z˄3 + 2i = 0.

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Question 1123448: Find all the solutions of the equation z˄6 + (2 + 2i)z˄3 + 2i = 0.
Answer by solver91311(24713) About Me  (Show Source):
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Let , then



Using the Quadratic formula:



with a multiplicity of 2. Verification of this step left as an exercise for the student.

Hence





But this must be multiplied by the three cube roots of unity to obtain the three roots of the cubic which, considering the multiplicity of the quadratic in gives the 6 roots of the original 6th-degree equation.








John

My calculator said it, I believe it, that settles it